dorsal/arxiv
View SchemaWFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport
| Authors | Qiangwei Peng, Zihan Wang, Junda Ying, Yuhao Sun, Qing Nie, Lei Zhang, Tiejun Li, Peijie Zhou |
|---|---|
| Categories | |
| ArXiv ID | 2601.06810vv1 |
| URL | https://arxiv.org/abs/2601.06810 |
| License | http://creativecommons.org/licenses/by-nc-sa/4.0/ |
Abstract
The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time.
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"date_created": "2026-02-17T05:53:08.767000Z",
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"abstract": "The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time.",
"arxiv_id": "2601.06810",
"authors": [
"Qiangwei Peng",
"Zihan Wang",
"Junda Ying",
"Yuhao Sun",
"Qing Nie",
"Lei Zhang",
"Tiejun Li",
"Peijie Zhou"
],
"categories": [
"cs.LG",
"cs.AI",
"math-ph",
"math.MP"
],
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
"title": "WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport",
"url": "https://arxiv.org/abs/2601.06810",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5b5a3129-8a66-4803-90b6-263f8ede7041",
"id": "arXiv Dataset",
"type": "Model",
"variant": "snapshot-2026-01-17",
"version": "0.1.0"
},
"user_id": 1000002
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